We explore the superconducting state of hole-doped cuprates by
electronic
Raman scattering as a function of both temperature and doping level.
We observe a loss of coherent quasi-particles in the anti-nodal
region and
show that coherent Bogoliubov quasiparticles are confined around
the nodes.
This contrasts to conventional superconductors where
superconductivity
develops uniformly along the normal-state Fermi surface.
We define the fraction of coherent Fermi surface, f$_{c}$ around
the nodes
for which quasi-particles are well defined and superconductivity
sets in. We
establish that T$_{c} \quad \propto $ f$_{c}\Delta _{max}$. $\Delta
_{max}$ is the maximum amplitude of the d-wave superconducting
gap. This
new relation differs from the standard BCS theory and gives us
some clues
for increasing T$_{c}$ in the cuprates. S. Blanc et al. Phys. Rev. B
\textbf{82}, 144516 (2010); S. Blanc et al. Phys. Rev. B
\textbf{80}, 140502
(2009).

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2011.MAR.X25.1